Due to present computational limitations, migration by the one-way wave equation remains an integral tool in seismic exploration. For the realistic interpretation of common image point gathers, it is necessary that migration be free from artifacts from caustics and turning waves. In order to permit situations where turning waves occur, we perform our migration on specially chosen curvilinear coordinates where waves do not travel horizontally. We present an implementation of the curvilinear one-way wave equation using a rational approximation and discuss its application in migration velocity analysis, as well as transmission and reflection tomography.